Before to learn prime triplets we should must know the prime numbers, and composite numbers.
Prime numbers are those numbers which are having factors or divisors as 1 and the number itself.
They starts from 2, 3, 5, 7, 11… and so on. 2 is the smallest even prime number. 0 and 1 are neither prime nor composite numbers.
The composite numbers are the numbers whose factors or divisors are other than 1 and the number itself also. 4, 6, 8, 9… and so on are the composite numbers which are having more than 1 and the number itself as factors.
Now, we learn what prime triplets are and how they are defined. In the word prime triplets, the two meanings are there. One is prime and the second is triplet that means these are the prime numbers and not in pair but in the triplet form i.e. pair of three prime numbers having some specific properties.
Prime triplet:
Prime triplets are the group of three prime numbers, in which there is a fixed difference in between the first and third number which is 6 always.
Let us suppose, p be the first prime number then the third prime number must be (p + 6).
Hence, the prime triplet is in the form: (p, p+2, p+6) or (p, p+4, p+6)
For example:
1) (5, 7, 11) is the prime triplet. Because 5, 7 and 11 are the prime numbers.
Here, p = 5, p+2 = 5+2 = 7 and p+6 =11
Thus, it takes the form of prime triplet, hence (5, 7, 11) is the prime triplet.
2) (7, 11, 13)
Here, 7, 11 and 13 are the prime numbers.
And, p = 7, p+4= 7+4= 11 and p+6 = 7+6 =13
Hence, (7, 11, 13) forms the prime triplet.
3) (11, 13, 17)
Here, 11, 13 and 17 are the prime numbers.
And, p = 11, p+2 = 11+2 = 13 and p+6 = 11+6 = 17
Hence, (11, 13, 17) forms the prime triplet.
Note:
- (2, 3, 5) is not the prime triplet although 2, 3 and 5 are prime numbers.
Because it cannot be written in prime triplet form.
- Also, (3, 5, 7) is not the prime triplet although 3, 5 and 7 are prime numbers.
Because it cannot be written in the form of prime triplet.
Very good for 6th